Question

Daniela recorded the low temperatures during the school day last week and this week. Her results are shown in the table below.

Low Temperatures during the School Day This Week and Last Week
Low Temperatures
This Week (Degrees Fahrenheit)

42

38

45

46

39
Low Temperatures
Last Week (Degrees Fahrenheit)

56

58

52

62

62

Daniela used the steps below to find a relationship between the difference in the mean temperatures and the mean absolute deviations of the data sets.

This Week Last Week

Step 1
Find the mean.
StartFraction 42 + 38 + 45 + 46 + 39 over 5 EndFraction = 42
Find the mean.
StartFraction 56 + 58 + 52 + 62 + 62 over 5 EndFraction = 58

Step 2
Find the mean absolute deviation.
StartFraction StartAbsoluteValue 42 minus 42 EndAbsoluteValue + StartAbsoluteValue 38 minus 42 EndAbsoluteValue + StartFraction StartAbsoluteValue 45 minus 42 EndAbsoluteValue + StartFraction StartAbsoluteValue 46 minus 42 EndAbsoluteValue + StartFraction StartAbsoluteValue 39 minus 42 EndAbsoluteValue over 5 EndFraction = 2.8
Find the mean absolute deviation.
StartFraction StartAbsoluteValue 56 minus 58 EndAbsoluteValue + StartAbsoluteValue 58 minus 58 EndAbsoluteValue + StartFraction StartAbsoluteValue 52 minus 58 EndAbsoluteValue + StartFraction StartAbsoluteValue 62 minus 58 EndAbsoluteValue + StartFraction StartAbsoluteValue 62 minus 58 EndAbsoluteValue over 5 EndFraction = 3.2
Step 3 Find the ratio of the differences of the means compared to the mean absolute deviation.
StartFraction 42 over 2.8 EndFraction = 15 Find the ratio of the differences of the means compared to the mean absolute deviation.
StartFraction 58 over 3.2 EndFraction = 18.125
Step 4 The difference in the means is about StartFraction 15 + 18 over 2 EndFraction = 16.5 times the mean absolute deviations.

In which step did Daniela make the first error?