Basic Statics 6-8-2011

1.Using the frequency distribution given, construct a frequency polygon. Class Boundaries Frequency 95.5 - 100.5      2 100.5 - 105.5 8 105.5 - 110.5 18 110.5 - 115.5 13 115.5 - 120.5 7 120.5 - 125.5 1 125.5 - 130.5 1

Find the midpoints of each class. Recall that midpoints are found by adding the upper and lower boundaries and dividing by 2:
95.5 + 100.5 2  = 98		100.5 + 105.5 2  = 103
and so on. The midpoints are
Class Boundaries Midpoints Frequency 95.5 - 100.5 98 2 100.5 - 105.5 103 8 105.5 - 110.5 108 18 110.5 - 115.5 113 13 115.5 - 120.5 118 7 120.5 - 125.5 123 1 125.5 - 130.5 128 1
Draw the x and y axes. Label the x axis with the midpoint of each class, and then use a suitable scale on the y axis for the frequencies.
Using the midpoints for the x values and the frequencies as the y values, plot the points.
Connect adjacent points with line segments. Draw a line back to the x axis at the beginning and end of the graph, at the same distance that the previous and next midpoints would be located.

Construct a histogram to represent the data shown below for the record high temperatures for each of the 50 states.  Class boundaries   Frequency  99.5-104.5           1 104.5-109.5     4 109.5-114.5     8 114.5-119.5     8 119.5-124.5     19 124.5-129.5     5 129.5-134.5     4 134.5-139.5     1 Is the given histogram correct?

Draw and label the x and y axes. The x axis is always the horizontal axis, and the y axis is always the vertical axis.

Represent the frequency on the y axis and the class boundaries on the x axis.

Using the frequencies as the heights, draw vertical bars for each class.

No, the given graph does not match the graph we constructed.

Top of Form

Bottom of Form

These data represent the record high temperatures for each of the 50 states. Construct a grouped frequency distribution for the data using 7 classes. 112 100 127 120 134 118 105 110 109 112 110 118 117 116 118 122 114 114 105 109 107 112 114 115 118 117 118 122 106 110 116 108 110 121 113 120 119 111 104 111 120 113 120 117 105 110 118 112 114 114 What is the cumulative frequency of the class 124.5 - 129.5?

The procedure for constructing a grouped frequency distribution for numerical data follows.
Determine the classes. Find the highest value and the lowest value: H = 134 and L = 100. Find the range: R = highest value - lowest value = H - L, so R = 134 - 100 = 34 Select the number of classes desired (usually between 5 and 20). In this case, 7 is arbitrarily chosen.
Find the class width by dividing the range by the number of classes. Width =  R number of classes  = 4.9 (rounded to one decimal place)
Round the answer up to the nearest whole number if there is a remainder: 4.9 5. (Rounding up is different from rounding off. A number is rounded up if there is any remainder when dividing. For example, 85 6 = 14.167 and is rounded up to 15. Also, 53 4 = 13.25 and is rounded up to 14.)
Select a starting point for the lowest class limit. This can be the smallest data value or any convenient number less than the smallest data value. In this case 100 is used. Add the width to the lowest score taken as the starting point to get the lower limit of the next class. Keep adding until there are 7 classes, 100, 105, 110, etc. Subtract one unit from the lower limit of the second class to get the upper limit of the first class. Then add the width to each upper limit to get all the upper limits. 105 - 1 = 104 The first class is 100 - 104, the second class is 105 - 109, etc. Find the class boundaries by subtracting 0.5 from each lower class limit and adding 0.5 to each upper class limit: 99.5 - 104.5, 104.5 - 109.5, etc.
Tally the data.
Find the numerical frequencies from the tallies. A cumulative frequency column can be added to the distribution by adding the frequency in each class to the total of the frequencies of the classes preceding that class, such as 0 + 2 = 2, 2 + 8 =10, 10 + 18 = 28, and 28 + 13 = 41. The completed frequency distribution is Class Limits Class boundaries Tally Frequency Cumulative Frequency 100 - 104 99.5 - 104.5 2 2 105 - 109 104.5 - 109.5 8 10 110 - 114 109.5 - 114.5 18 28 115 - 119 114.5 - 119.5 13 41 120 - 124 119.5 - 124.5 7 48 125 - 129 124.5 - 129.5 1 49 130 - 134 129.5 - 134.5 1 50
The frequency distribution shows that the cumulative frequency of the class 124.5 - 129.5 is 49. These data represent the record high temperatures for each of the 50 states. Construct a grouped frequency distribution for the data using 7 classes. 112 100 127 120 134 118 105 110 109 112 110 118 117 116 118 122 114 114 105 109 107 112 114 115 118 117 118 122 106 110 116 108 110 121 113 120 119 111 104 111 120 113 120 117 105 110 118 112 114 114 What is the frequency of the class 119.5 - 124.5?
Twenty-five army inductees were given a blood test to determine their blood type. The data set is A O AB AB O AB O B AB B B B O A O A O O O AB AB A O B A Construct a frequency distribution for the data. What is the frequency in the class of type O?

Since the data are categorical, discrete classes can be used. There are four blood types: A, B, O and AB. These types will be used as the classes for the distribution. The procedure for constructing a frequency distribution for categorical data is given next.

Make a table as shown. A B C D Class Tally Frequency Percent A B O AB

Tally the data and place the results in column B.

Count the tallies and place the results in column C.

Find the precentage of values in each class by using the formula % =  f n   100% where f = frequency of the class and n = total number of values. For example, in the class of type A blood, the percentage is % =  5 25   100% = 20% Percentages are not normally a part of a frquency distribution, but they can be added since they are used in certain types of graphical presentations, such as pie graphs.

Find the totals for the columns C and D (see completed table). A B C D Class Tally Frequency Percent A 5 20 B 5 20 O 9 36 AB   6  24 Total 25 100

For the sample, we have 9 people with type O blood.

The data shown here represent the number of miles per gallon that 30 selected four-wheel-drive sports utility vehicles obtained in city driving.

Construct a frequency distribution.

12 17 12 14 16 18 16 18 12 16 17 15 15 16 12 15 16 16 12 14 15 12 15 15 19 13 16 18 16 14

What is the frequency of the class 11.5 - 12.5?

The number of stories in two selected samples of tall buildings in Los Angeles and Philadelphia are shown. Construct a back-to-back stem and leaf plot, and compare the distributions. Los Angeles Philadelphia 23 42 29 37 54 56 22 34 21 46 38 36 44 40 34 42 52 30 43 44 Does Los Angeles have more 40 story buildings than Philadelphia?

Arrange the data for both sets in order.
Construct a stem and leaf plot using the same digits as stems. Place the digits for the leaves for Los Angeles on the left side of the stem and the digits for the leaves for Philadelphia on the right side.
Los Angeles Philadelphia  9   3   2   1   2   8   7   6   4  3  0   4   4   2   0  4  2   3   4   6   4  5  2   6
Compare the distributions. The buildings in Los Angeles have a large variation in the number of stories per building. Philadelphia has more 40 story buildings than Los Angeles. Therefore the answer is no.
Construct an ogive for the frequency distribution below. Class Boundaries Frequency 99.5 - 104.5      2 104.5 - 109.5 6 109.5 - 114.5 16 114.5 - 119.5 12 119.5 - 124.5 9 124.5 - 129.5 4 129.5 - 134.5 1

Find the cumulative frequency for each class.

Class Boundaries Cumulative Frequency 99.5 - 104.5      2 104.5 - 109.5 8 109.5 - 114.5 24 114.5 - 119.5 36 119.5 - 124.5 45 124.5 - 129.5 49 129.5 - 134.5 50

Draw the x and y axes. Label the x axis with the class boundaries. Use an appropriate scale for the y axis to represent the cumulative frequencies. (Depending on the numbers in the cumulative frequency columns, scales such as 0, 1, 2, 3, . . ., or 5, 10, 15,20, . . ., or 1000, 2000, 3000, . . . can be used. Do not label the y axis with the numbers in the cumulative frequency column.) In this example, a scale of 0, 5, 10, 15, . . . will be used.

Plot the cumulative frequency at each upper class boundary. Upper boundaries are used since the cumulative frequencies represent the number of data values accumulated up to the upper boudary of each class.

Starting with the first upper class boundary, 104.5, connect adjacent points with line segments. Then extend the graph to the first lower class boundary, 99.5 on the x axis. ALBANY STATE UNIVERSITY BASIC STATISTICS                                                                 TEST-1 (CHAPTER-1, 2)                                                                                                              Date: 1.   Define Population, Sample. 2.    Name and define two areas of statistics. 3.   Define bas ic sampling methods. 4.   What are the types of sampling? 5.   The average grade of a class is 90. Define    Descriptive / Inferential 6.   Allergy therapy makes bees go away. Define    Descriptive / Inferential 7.   Classify the variable 1.   Wal-Mart sold 100 TV sets in a weak in Albany area. Qualitative/ Quantitative 2.   All of Basic Statistics students in ASU are hard workers. Qualitative/ Quantitative 3.   Number of toys sold in a store.  Discrete/ continuous 4.   The average age of a class. Discrete/ continuous 8.   What are the boundaries of 25.6 ounces? a)   25-26  b)25.55-25.65   c)25.5-25.7  d)20-39 9.   A researcher divided subjects into two groups according to gender and then selected members from each group for her sample. What sampling method was heresearcher using. a)   Cluster  b) Random  c) Systematic  d) stratified      10.   Classify each sample as random, systematic, stratified, or cluster. a)   In ASU, all teachers from two buildings are interviewed to determine whether they believe the students have less homework to do now than in previous years. b)   Every 5 th player is selected for soccer game in ASU. c)   Statistics students are selected to determine annual graded. d)   Every 100 th manufactured item is checked to determine its quality. e)   In USPS MAIL carriers of Albany city are divided into four groups according to gender and according to whether they walk or ride on their routes. Then 10 are selected from each group and interviewed to determine whether they have been by a dog in the last year. 11.  List five reasons for organizing data in to a frequency distribution. 12.  Find class limits, upper limits. Lower limits. Upper bounds. Lower bounds. Mid point. Class Limits Class boundaries class limits midpoints    Frequency Cumulative Frequency 100 - 104 2 105 - 109 8 110 - 114 18 115 - 119 13 120 - 124 7 125 - 129 1 130 - 134 1 13.  ­­­idnt_______________________s.lower limits. upper uency distribution. 13.  og in the last year. 13.  e students have less homework to di n Twenty-five army inductees were given a blood test to determine their blood type. The data set is A O AB AB O AB O B AB B B B O A O A O O O AB AB A O B A Construct a frequency distribution for the data. What is the frequency in the class of type O? 14.  Since the data are categorical, discrete classes can be used. There are four blood types: A, B, O and AB. These types will be used as the classes for the distribution. The procedure for constructing a frequency distribution for categorical data is given next. 14. The data shown here represent the number of miles per gallon that 30 selected four-wheel-drive sports utility vehicles obtained in city driving. Construct a frequency distribution. 12 17 12 14 16 18 16 18 12 16 17 15 15 16 12 15 16 16 12 14 15 12 15 15 19 13 16 18 16 14 What is the frequency of the class 11.5 - 12.5?