Question

a) Calculate the arithmetic mean, median and mode from the following frequency distribution. Data 410-419 420-429 430-439 440-449 450-459 460-469 470-479 Weight (in grams) No. of apples 14 20 42 54 45 18 7
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Answer 1

Answer:

I don't know the answer for this question because its is not in my mind

Explanation:

so I don't know if you have any questions or suggestions

Answer 2

Given:

Data for the weight of apples in grams and the number of apples in that range of weight.

To find:

Arithmetic mean, median, and mode of the given data.

Solution:

Table

weight      mid-point     frequency(x)     cumulative frq    mid-point * x

410-419         415                  14                        14                    5810

420-429       425                 20                       34                   8500

430-439       435                  42                        76                  18270

440-449       445                  54                       130                 24030

450-459       455                  45                       175                 20475

460-469       465                  18                        193                 8370

470-479        475                   7                         200                3325

Mean

The mean will be equal to the total weight of apples divided by the total number of apples.

mean = ∑(mid-point * x)/ ∑x

mean = $\frac{88780}{200}$

mean = 443.9

Median

for the median, we will first assume the median group.

From the cumulative frequency values, we can see that the estimated mean group will be  440-449.

median = L + $\frac{(n/2) - B}{G}$ × w

L = lower boundary of median group = 440

n = total number of apples = 200

B = cumulative frequency of group before median group = 76

G = frequency of median group = 54

w = group width = 10

Median = 440+ $\frac{100 - 76}{54}$ × 10

median = 440 + 4.44

median = 444.44

Mode

For mode, we will first assume the modal group, the group with the highest frequency.

From the table, we can say that the modal group will be 440-449.

Mode = L + $\frac{f_{m} - f_(m-1) }{(f_m - f_(m-1)) + ( f_m - f_(m+1))}$ × w

L = the lower class boundary of the modal group = 440

$f_m$ = frequency of modal group = 54

$f_(m-1)$ = frequency of group before the modal group = 42

$f_(m+1)$ = frequency of group after the modal group = 45

w = group width = 10

mode = 440 + $\frac{54 - 42}{(54-42) + (54-45)}$ x 10

mode = 440 + 5.71

mode = 445.71

The arithmetic mean will be 443.9

The arithmetic median will be 444.44

The arithmetic mode will be = 445.71