Answer: D) 65.56
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Explanation:
The interval [tex]40 \le x < 50[/tex] 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 [tex]50 \le x < 60[/tex] 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
