Question

Find the mean of the data summarized in the given frequency distribution. Compare the computed mean to the actual mean of 51.1 degrees. Low Temperature ​(◦​F) 40−44 45−49 50−54 55−59 60−64 Frequency 3 6 13 7

Answer 1

Answer:

$Mean = 53.25$

Step-by-step explanation:

Given

Low Temperature : 40−44 || 45−49 ||  50−54 || 55−59 || 60−64

Frequency: --------------- 3 -----------6----------- 1-----------3--- -----7

Required

Determine the mean

The first step is to determine the midpoints of the given temperatures

40 - 44:

$Midpoint = \frac{40+44}{2}$

$Midpoint = \frac{84}{2}$

$Midpoint = 42$

45 - 49

$Midpoint = \frac{45+49}{2}$

$Midpoint = \frac{94}{2}$

$Midpoint = 47$

50 - 54:

$Midpoint = \frac{50+54}{2}$

$Midpoint = \frac{104}{2}$

$Midpoint = 52$

55- 59

$Midpoint = \frac{55+59}{2}$

$Midpoint = \frac{114}{2}$

$Midpoint = 57$

60 - 64:

$Midpoint = \frac{60+64}{2}$

$Midpoint = \frac{124}{2}$

$Midpoint = 62$

So, the new frequency table is as thus:

Low Temperature : 42 || 47 ||  52 || 57 || 62

Frequency: ----------- 3 --||- -6-||- 1-||- --3- ||--7

Next, is to calculate mean by

$Mean = \frac{\sum fx}{\sum x}$

$Mean = \frac{42 * 3 + 47 * 6 + 52 * 1 + 57 * 3 + 62 * 7}{3+6+1+3+7}$

$Mean = \frac{1065}{20}$

$Mean = 53.25$

The computed mean is greater than the actual mean