Find the mean for the following frequency tables. (Round your answers to one decimal place.)(a)         Grade Frequency49.5–59.5 259.5–69.5 369.5–79.5 979.5–89.5 1489.5–99.5 5 (b)         Daily Low Temperature Frequency49.5–59.5 5159.5–69.5 3269.5–79.5 1579.5–89.5 189.5–99.5 0 (c)         Points per Game Frequency49.5–59.5 1459.5–69.5 3269.5–79.5 1579.5–89.5 2389.5–99.5 2

To find the mean of a frequency table, we need to multiply each value by its frequency, sum these products, and then divide by the total frequency.

(a) For the Grade frequency table:

First, find the midpoint of each interval by adding the lower and upper bounds and dividing by 2. Then multiply each midpoint by its frequency:

(49.5+59.5)/2 * 2 = 109 (59.5+69.5)/2 * 3 = 193.5 (69.5+79.5)/2 * 9 = 670.5 (79.5+89.5)/2 * 14 = 1197 (89.5+99.5)/2 * 5 = 445

Sum these products: 109 + 193.5 + 670.5 + 1197 + 445 = 2615

The total frequency is 2 + 3 + 9 + 14 + 5 = 33

So, the mean is 2615 / 33 = 79.2 (rounded to one decimal place)

(b) For the Daily Low Temperature frequency table:

(49.5+59.5)/2 * 5 = 272.5 (59.5+69.5)/2 * 3 = 193.5 (69.5+79.5)/2 * 15 = 1117.5 (79.5+89.5)/2 * 1 = 84.5 (89.5+99.5)/2 * 0 = 0

Sum these products: 272.5 + 193.5 + 1117.5 + 84.5 + 0 = 1668

The total frequency is 5 + 3 + 15 + 1 + 0 = 24

So, the mean is 1668 / 24 = 69.5 (rounded to one decimal place)

(c) For the Points per Game frequency table:

(49.5+59.5)/2 * 1 = 54.5 (59.5+69.5)/2 * 3 = 193.5 (69.5+79.5)/2 * 15 = 1117.5 (79.5+89.5)/2 * 23 = 1935.5 (89.5+99.5)/2 * 2 = 189

Sum these products: 54.5 + 193.5 + 1117.5 + 1935.5 + 189 = 3490

The total frequency is 1 + 3 + 15 + 23 + 2 = 44

So, the mean is 3490 / 44 = 79.3 (rounded to one decimal place)

To find the mean of a frequency table, we need to multiply each value by its frequency, sum these products, and then divide by the total frequency.

(a) For the grades:

• The midpoint of each interval is calculated as (lower limit + upper limit) / 2.
• Multiply each midpoint by its frequency.
• Sum these products and divide by the total frequency.

Doing this, we get:

• (54.5 * 2) + (64.5 * 3) + (74.5 * 9) + (84.5 * 14) + (94.5 * 5) = 109 + 193.5 + 670.5 + 1183 + 472.5 = 2628.5
• Total frequency = 2 + 3 + 9 + 14 + 5 = 33
• Mean = 2628.5 / 33 = 79.7 (rounded to one decimal place)

(b) For the daily low temperature:

• (54.5 * 5) + (64.5 * 3) + (74.5 * 15) + (84.5 * 18) + (94.5 * 0) = 272.5 + 193.5 + 1117.5 + 1521 + 0 = 3104.5
• Total frequency = 5 + 3 + 15 + 18 + 0 = 41
• Mean = 3104.5 / 41 = 75.7 (rounded to one decimal place)

(c) For the points per game:

• (54.5 * 14) + (64.5 * 3) + (74.5 * 15) + (84.5 * 23) + (94.5 * 2) = 763 + 193.5 + 1117.5 + 1943.5 + 189 = 4206.5
• Total frequency = 14 + 3 + 15 + 23 + 2 = 57
• Mean = 4206.5 / 57 = 73.8 (rounded to one decimal place)