Mean Calculation for Mid Value and Frequency Data

To find the mean from the given data, we need to follow the steps mentioned below:

Step 1: Multiply each mid-value by its corresponding frequency to get the product.

Step 2: Add all the products obtained in step 1 to get the total sum of products.

Step 3: Add all the frequencies to get the total frequency.

Step 4: Divide the total sum of products obtained in step 2 by the total frequency obtained in step 3 to get the mean.

Now, let's apply these steps to the given data:

Mid Value | Frequency
--------- | ----------
25 | 5
35 | 8
45 | 16
55 | 19
65 | 13
75 | 4

Step 1: Multiply each mid-value by its corresponding frequency to get the product.

25 x 5 = 125
35 x 8 = 280
45 x 16 = 720
55 x 19 = 1045
65 x 13 = 845
75 x 4 = 300

Step 2: Add all the products obtained in step 1 to get the total sum of products.

125 + 280 + 720 + 1045 + 845 + 300 = 3315

Step 3: Add all the frequencies to get the total frequency.

5 + 8 + 16 + 19 + 13 + 4 = 65

Step 4: Divide the total sum of products obtained in step 2 by the total frequency obtained in step 3 to get the mean.

Mean = 3315 / 65 = 51

Therefore, the mean for the given data is 51.