Question 6 of 21intermediate🔧 ApplyNumerical3 marks

The table below shows the daily expenditure on food of 25 households in a locality.

Daily expenditure (in ₹)100 - 150150 - 200200 - 250250 - 300300 - 350
Number of households451222

Find the mean daily expenditure on food by a suitable method.

Correct Answer

To find the mean daily expenditure, we use the Direct Method because the class size is uniform and the values are manageable. First, we calculate the class mark (xix_i) for each class interval, which is the mid-point.

Daily expenditurefif_ixix_ifixif_i x_i
100 - 1504125500
150 - 2005175875
200 - 250122252700
250 - 3002275550
300 - 3502325650
Total∑fi=25\sum f_i = 25∑fixi=5275\sum f_i x_i = 5275

Using the formula: Mean =∑fixi∑fi= \frac{\sum f_i x_i}{\sum f_i}. Substituting the values: Mean =527525=211= \frac{5275}{25} = 211.

Thus, the mean daily expenditure on food is ₹ 211.

Exercise: EXERCISE 13.1 | Q: 6 | (Page 12)
For More Understanding

Explanation

The Direct Method is appropriate here as the class intervals are continuous and the calculation involves manageable numbers. The class mark (xix_i) is calculated for each interval by averaging the upper and lower limits. The sum of the product of frequencies and class marks (∑fixi\sum f_i x_i) is divided by the total number of households (∑fi\sum f_i) to find the mean.

Solution Steps

  1. Step 1: Calculate class marks (xix_i) for each interval: (100+150)/2=125(100+150)/2 = 125, (150+200)/2=175(150+200)/2 = 175, etc.

  2. Step 2: Calculate the product fixif_i x_i for each class: 4×125=5004 \times 125 = 500, 5×175=8755 \times 175 = 875, 12×225=270012 \times 225 = 2700, 2×275=5502 \times 275 = 550, 2×325=6502 \times 325 = 650.

  3. Step 3: Find the summations: ∑fi=25\sum f_i = 25 and ∑fixi=5275\sum f_i x_i = 5275.

  4. Step 4: Apply the mean formula: Mean =527525=211= \frac{5275}{25} = 211.

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