Essential Statistic Box-Plots and Standard Deviations Name:______

1.  The level of various substances in the blood influences our health. Here are the measurements of the level of phosphate in the blood of a patient, in milligrams of phosphate per deciliter of blood, made on 6 consecutive visits to a clinic.
5.6 5.2 4.6 4.9 5.7 6.4

  1. Find the mean of the data
  2. Determine the standard deviation
  3. Use the Stat button on your calculator to find the x and s, compare the results.

2.  Here are the scores on the Survey of Study Habits and Attitudes (SSHA) for 18 first-year college women:
154 109 137 115 152 140 154 178 101 103 126 126 137 165 165 129 200 148

  1. Find the 5 number summary for this data
  2. Create a box-plot
  3. Should we use the 5 number summary to explain the data or the x and s? Explain.

Height / Count / Height / Count / Height / Count
60 / 2 / 66 / 18 / 72 / 9
61 / 6 / 67 / 7 / 73 / 4
62 / 9 / 68 / 12 / 74 / 2
63 / 7 / 69 / 5 / 75 / 4
64 / 5 / 70 / 11 / 76 / 1
65 / 20 / 71 / 8

3.  The frequency table below shows the heights (in inches) of 130 choir members.

  1. Find the 5 number summary for this data
  2. Display the data with a box plot
  3. Find the x and s
  4. Display this data with a histogram
  5. Write a few sentences describing the distribution of the heights.

4.  For each lettered part, a through c, examine the two given sets of numbers. Without doing any calculations, decide which set has the larger standard deviation, and explain why. Then check by finding it by hand.
Set 1 Set 2

  1. 3, 5, 6, 7, 9 2, 4, 6, 8, 10
  2. 10, 14, 15, 16, 20 10, 11, 15, 19, 20
  3. 2, 6, 6, 9, 11, 14 82, 86, 86, 91, 94


To draw a boxplot, you need to first find five values:

(a) minimum (b) Q1 (first quartile) (c) median (d) Q3 (third quartile) (e) maximum

Then draw an appropriate scale and make the boxplot. The minimum, median and maximum should not be difficult to find. Finding the quartiles is more work:

(1) First, make sure numbers are in increasing order.

(2) Locate the median (or solve for the median)

(3) To find Q1 (first quartile): Find the median of ALL values that are below the median.

(4) To find Q3 (third quartile): Find the median of ALL values that are above the median.

Note: NEVER include the actual median in the data when finding the quartiles.

Find the 5-number summary and draw the boxplot for each data set.

5. n = 13 0 0 1 2 2 2 3 3 4 5 5 5 7

6. n = 12 0 0 1 2 2 2 3 3 4 5 5 7

7. n = 11 15 18 19 20 21 23 26 29 30 32 38

8. n = 10 53 56 65 68 72 78 85 86 88 93