Assessing Normality

If a graph of quantitative data looks symmetric, single peaked, and bell-shaped, then the distribution is approximately normal. We don't need to check anything else.

• True

• False

If the mean and median of a data set are roughly equal, then the data is probability symmetric, but not necessarily normal.

• True

• False

Does this dotplot lead you to believe that the distribution is approximately normal?

• Yes, the graph is symmetrical, single peaked and bell-shaped.

• No, the graph is skewed right.

• No, the graph is skewed left.

Here are the ages of 10 people at a party. 14 14 18 18 19 21 35 42 65 80 Calculate the mean and median using a statistical calculator or by hand. Are they close?

• Mean = 20, Median = 32.6 They are not close

• Mean = 35, Median = 19 They are not close

• Mean = 31, Median = 29 They are close

• Mean = 32.6, Median = 20 They are not close

• Mean = 19.8, Median = 21 They are close

Here are the ages of 10 people at a party. 14 14 18 18 19 21 35 42 65 80 In the last question, the mean was found to be 32.6 and the median was 20. Since the mean is quite a bit higher than the median, what is most likely the shape of the distribution of ages?

• Symmetric

• Uniform

• Skewed Left

• Skewed Right

Here are the ages of 10 people at a party. 14 14 18 18 19 21 35 42 65 80 In your notebook, make a dot plot of the data. What shape does it have? Note: This answer should be the same as the last question!

• Symmetric

• Skewed Left

• Skewed Right

The following data set of 10 values has a mean = 10 and a SD = 6.77 2 2 4 4 10 10 15 15 19 19 Create the interval MEAN +/- 1 SD by subtracting 6.77 from the10 to get the low end and then adding 6.77 to 10 to get the high end.

• 3.23 to 16.77

• 3.54 to 9.56

• 2.15 to 10.28

This is the same dataset as the previous questions (ages of people at a party). What percent of the values are in the interval from 3.23 to 16.77? 2 2 4 4 10 10 15 15 19 19 Hint: The green number are in the interval, the red ones are not.

• 50%

• 60%

• 68%

• 80%

Here are the ages of the first 45 presidents when they took office: 42 43 46 46 47 48 49 49 50 51 51 51 51 51 52 52 54 54 54 54 54 55 55 55 55 56 56 56 57 57 57 57 58 60 61 61 61 61 64 64 65 68 69 70. What percent of the ages lie in the interval from 41.84 to 68.12?

• 95.55%

• 93.33%

• 97.66%

• 98.22%

Answer explanation

All but two of the ages are in this interval. 43/45 = 0.955555 or about 95.55%

Here are the lengths in feet of 44 great white sharks: 9.4 12.1 12.2 12.3 12.4 12.6 13.2 13.2 13.2 13.2 13.5 13.6 13.6 13.8 14.3 14.6 14.7 14.9 15.2 15.3 15.7 15.7 15.8 15.8 16.1 16.2 16.2 16.4 16.4 16.6 16.7 16.8 16.8 17.6 17.8 17.8 18.2 18.3 18.6 18.7 18.7 19.1 19.7 22.8 The mean is 15.586 ft and the SD is 2.55 ft. Calculate an interval: Mean +/- 1 SD

• 14.024 to 18.935

• 13.036 to 18.136

• 12.937 to 19.054

• 14.223 to 17.954