Chapter 3 Review
Part I
Use the given sample data to answer #1-5:
49 52 52 52 74 67 55 55
1) Find the mean, mode, median
2) Find the range and midrange
3) Find the 5 # summary
4) Find and
5) Find the std. dev. using the shortcut formula; find the variance
6) Construct the stem-and-leaf plot and a boxplot.
7) Which is better: A score of 580 on a test with a mean of 430 and a standard deviation of 130, or a score of 93 on a test with a mean of 75 and a standard deviation of 15? Explain your choice.
Use the frequency table below to answer #7-9:
X / F0-8 / 2
9-17 / 8
18-26 / 5
27-35 / 10
36-44 / 4
45-53 / 1
8) Find the mean of the frequency table.
9) What is the class width?
10) Add a column for the cumulative frequency that corresponds to the frequency table.
11) If a set of data has a mean of 9.7, what is the mean after 20 has been added to each score?
12) If a set of data has a standard deviation of 5.8, what is the standard deviation after 20 has been added to each score?
Part II
Consider the following data set to answer questions #11-21:
11th graders:
97 66 73 75 86 86 91 61 72 96 85 73
95 93 76 76 83 86 86 87 84 83 82 78
83
12th graders:
64 96 83 83 79 98 89 82 95 94 85 86
96 83 94 93 78 86 82 73
Calculate the following items to the nearest hundredth for each data set:
13) Mean, Standard deviation
14) 5 # Summary
15) Range, Midrange, Mode, IQR
16) Calculate for outliers
17) Draw boxplots for each grade level. Place the 12th grade above the 11th grade. Be sure to label points/axes as necessary.
18) Make a back-to-back stemplot of the data. Put the 11th grade on the left and the 12th grade on the right. Use the actual scores – do not group them into intervals.
19) Make a frequency table with 8 intervals for the 11th grade data.
20) Make another column on your frequency table for the 11th grade and label it cumulative frequency and fill in the appropriate numbers.
21) What is the z-score for an 87 in the 11th grade group?
22) What is the percentile for a 12th grade score of 79?
23) Are the 11th grade scores skewed? If so, in what direction?
Part I Solutions
1) 57, 52, 53.5
2) 25, 61.5
3) 49, 52, 53.5, 61, 74
4) 26528, 207936
5) 8.7, 76.7
6)
4 | 9
5 | 22255
6 | 7
7 | 4
7) Z=(580-430)/130 = 1.15; Z = (93-75)/15=1.2; The second one is better.
8) First, find the class midpoints for X: 4, 13, 22, 31, 40, 49. Put these in L1. Put the frequencies in L2. Program L3 = L1*L2. Sum up L3. Sum up L2. Divide SumL3 by Sum L2 = 24.7.
9) 9
10)
X / f / cf0-8 / 2 / 2
9-17 / 8 / 10
18-26 / 5 / 15
27-35 / 10 / 25
36-44 / 4 / 29
45-53 / 1 / 30
11) 29.7 (it will go up by 20)
12) 5.8 (it will not change)
Part II Solutions
13) 11th Graders: Mean 82.12, Standard deviation 9.1119 ; 12th graders: Mean 85.95, Std. Dev. 8.6965
14) 5 # Summary: 11th graders: 61 75.5 83 86.5 97 12th graders 64 82 85.5 94 98
15) 11th Graders: Range 36 , Midrange 79, Mode 86, IQR 11 12th graders: Range 34 , Midrange 81, Mode 83, IQR 12
16) Outliers 11th graders: 8; 12th graders: None
17) Draw boxplots for each grade level. Place the 12th grade above the 11th grade. Be sure to label points/axes as necessary.
18) Make a back-to-back stemplot of the data. Put the 11th grade on the left and the 12th grade on the right.
12th graders 11th Graders
4 6 1
6 6
3 7 233
98 7 5668
33322 8 23334
9665 8 566667
443 9 13
8665 9 567
19) Make a frequency table with 8 intervals for the 11th grade data.
Range: (97-61)/8=4.5, round to 5.
Class / Frequency60-64 / 1
65-69 / 1
70-74 / 3
75-79 / 4
80-84 / 5
85-89 / 6
90-94 / 2
95-99 / 3
20) Make another column on your frequency table for the 11th grade and label it cumulative frequency and fill in the appropriate numbers.
Class / Frequency / Cum. Frequency60-64 / 1 / 1
65-69 / 1 / 2
70-74 / 3 / 5
75-79 / 4 / 9
80-84 / 5 / 14
85-89 / 6 / 20
90-94 / 2 / 22
95-99 / 3 / 25
21) Z-score for an 87 in the 11th grade group: Z=(87-82.12)/9.111=.5356
22) Percentile for a 12th grade score of 79: (3/20)*100=15th percentile
23) No, the 11th grade scores are roughly symmetric.