Measures of Central Tendency Long Answer | University of Southern Mississippi

University:
University of Southern Mississippi
Course:
PSY 360 | Introduction to Statistics
Academic year:

2022
Views:

393

Pages:

6
Author:

Reynaldo Wong

LONG ANSWER QUESTION 1. If the arithmetic mean of the data given below is 28, find (a) the missing frequency and (b) the median of the series Answer: (a) Let the missing frequency br f1. Arithmetic Mean = 28 or 2240 -2100 = 35f1 = 28f1 or 140 = 7f1 f1 = 20 Hence, the missing frequency is 20. (b) So, the Median class = Size of (N2)th item = 50th term. 50th item lies in the 57th cumulative frequency and the corresponding class interval is 20-30. 2. The size of land holdings of 380 families in a village is given below. Find the median size of land holdings. Answer: So, the median class = Size of (N2) th item = 190 item 190th lies in the 129 th cumulative frequency and the corresponding class interval is 200-300. Median size of land holdings = 241.22 acres 3. The following series relates to the daily income of workers employed in a firm. Compute (a) highest income of lowest 50% workers, (b) minimum income earned by the top 25% workers and (c) maximum income earned by lowest 25% workers. Answer: (a) Highest income of lowest 50% workers will be given by the median. Σf = N = 65 Median class = Size of (N2)th item = Size of (652)th item=325 th item 32.5th item lies in the 50th cumulative frequency and the corresponding class interval is 24.5 – 29.5. (b) Minimum income earned by top 25% workers will be given by the lower quartile Q1. Class interval of Q1 = (N4)th item = (654)th item = 1625th item 16.25th item lies in the 30th cumulative frequency and the corresponding class interval is 19.5 – 24.5 (c) Maximum income earned by lowest 25% workers will be given by the upper quartile Q3. Class interval of Q3 = (N4)th item = 3(654)th item = 3 × 1625th item = 48.75th item 48.75th item lines in 50th item and the corresponding class interval is 24.5-29.5. 4. The following table gives production yield in kg per hectare of wheat of 150 farms in a village. Calculate the mean, median and mode production yield. Answer: (i) Mean (ii) Median (iii) Mode Grouping Table Analysis Table