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The number of students absent in a cla...

The number of students absent in a class were recorded every day for 120 days and the information is given in the following frequency table. Then mean number of students absent per day is
`{:("No. of student absent",0,1,2,3,4,5,6,7),("No. of days ",1,4,10,50,34,15,4,2):}`

A

`3 . 325`

B

`3 . 425`

C

`3. 525`

D

`4 . 525`

Text Solution

AI Generated Solution

The correct Answer is:
To find the mean number of students absent per day based on the given frequency table, we will follow these steps: ### Step 1: Understand the Frequency Table We have the following data: - No. of students absent (x): 0, 1, 2, 3, 4, 5, 6, 7 - No. of days (f): 1, 4, 10, 50, 34, 15, 4, 2 ### Step 2: Create a New Column for \( f_i \times x_i \) We will calculate \( f_i \times x_i \) for each value: - For \( x = 0 \): \( f = 1 \) → \( 0 \times 1 = 0 \) - For \( x = 1 \): \( f = 4 \) → \( 1 \times 4 = 4 \) - For \( x = 2 \): \( f = 10 \) → \( 2 \times 10 = 20 \) - For \( x = 3 \): \( f = 50 \) → \( 3 \times 50 = 150 \) - For \( x = 4 \): \( f = 34 \) → \( 4 \times 34 = 136 \) - For \( x = 5 \): \( f = 15 \) → \( 5 \times 15 = 75 \) - For \( x = 6 \): \( f = 4 \) → \( 6 \times 4 = 24 \) - For \( x = 7 \): \( f = 2 \) → \( 7 \times 2 = 14 \) ### Step 3: Summarize the Results Now we summarize the results of \( f_i \times x_i \): - \( f_i \times x_i \): 0, 4, 20, 150, 136, 75, 24, 14 ### Step 4: Calculate the Summation of \( f_i \times x_i \) Now we add these values: \[ \text{Summation of } (f_i \times x_i) = 0 + 4 + 20 + 150 + 136 + 75 + 24 + 14 = 423 \] ### Step 5: Calculate the Summation of \( f_i \) Next, we calculate the total number of days (which is the summation of \( f \)): \[ \text{Summation of } f = 1 + 4 + 10 + 50 + 34 + 15 + 4 + 2 = 120 \] ### Step 6: Use the Mean Formula Now we can use the formula for the mean: \[ \text{Mean} (x̄) = \frac{\sum (f_i \times x_i)}{\sum f_i} = \frac{423}{120} \] ### Step 7: Calculate the Mean Now we perform the division: \[ x̄ = \frac{423}{120} \approx 3.525 \] ### Conclusion The mean number of students absent per day is approximately **3.525**. ---
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