Question

Estimate the mean exam score for the 50 students in Prof. Burke's class.

Score

f

40 but less than 50

21



50 but less than 60

39



60 but less than 70

40



70 but less than 80

34



80 but less than 90

28



Total

162



Group of answer choices

63.78

62.34

64.89

65.56

Answer 1

Answer: D) 65.56

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Step-by-step explanation:

The interval
`40 \le x < 50` has the midpoint (40+50)/2 = 90/2 = 45 which represents the average value from this interval. We don't know what the exact 21 values are from this interval, but the best guess we can make is each value is on average 45.

Similarly, the interval
`50 \le x < 60` has the midpoint (50+60)/2 = 110/2 = 55 which represents the average value in this interval.

The set of all midpoints is: {45, 55, 65, 75, 85}. You start at 45 and add 10 to each term to get the next term. Let's say x represents the midpoint. We'll multiply each x value with its corresponding frequency (f) to get a new column of values you see in the table below.

For example, in the first row, we have 45*21 = 945

Add up everything in the x*f column and we'll get this sum:

945+2145+2600+2550+2380 = 10,620

We'll divide this over the total frequency, which is the sum of the frequency column (21+39+40+34+28 = 162)

We then arrive at this estimated final answer: (10,620)/(162) = 65.55555... where the '5's go on forever. This rounds to 65.56