We read your photo as:

To calculate the mean and standard deviation from the given frequency distribution, we will use the following formulas:

Mathematics

ScanSolve AI Answer

Answers

2 parts
a

Mean=7.30\text{Mean} = 7.30

b

Standard Deviation=2.04\text{Standard Deviation} = 2.04

Step-by-step solution

8 steps

To calculate the mean and standard deviation from the given frequency distribution, we will use the following formulas:
Mean (xˉ\bar{x}) xˉ=∑fx∑f\bar{x} = \frac{\sum fx}{\sum f}
Standard Deviation (σ\sigma) σ=∑fx2∑f−(∑fx∑f)2\sigma = \sqrt{\frac{\sum fx^2}{\sum f} - \left(\frac{\sum fx}{\sum f}\right)^2}
First, let's create a table to organize the calculations for fxfx and fx2fx^2.
The total number of students is ∑f=50\sum f = 50.

Hours per day (xx)Number of students (ff)fxfxx2x^2fx2fx^2
45201680
573525175
653036180
796349441
8129664768
943681324
10330100300
11555121605
Total503652873

From the table, we have:
∑f=50\sum f = 50
∑fx=365\sum fx = 365
∑fx2=2873\sum fx^2 = 2873

Part a· 3 steps

Mean

  1. Use the formula for the mean.

    xˉ=∑fx∑f\bar{x} = \frac{\sum fx}{\sum f}
  2. Substitute the calculated values into the formula.

    xˉ=36550\bar{x} = \frac{365}{50}
  3. Calculate the mean.

    xˉ=7.3\bar{x} = 7.3

    The mean is 7.30 hours (correct to two decimal places).

    Mean=7.30\boxed{\text{Mean} = 7.30}

Part b

Standard Deviation=2.04\text{Standard Deviation} = 2.04

Standard Deviation

  1. Use the formula for the standard deviation.

    σ=∑fx2∑f−(∑fx∑f)2\sigma = \sqrt{\frac{\sum fx^2}{\sum f} - \left(\frac{\sum fx}{\sum f}\right)^2}
  2. Substitute the calculated values into the formula.

    σ=287350−(36550)2\sigma = \sqrt{\frac{2873}{50} - \left(\frac{365}{50}\right)^2}
  3. Perform the division and squaring.

    σ=57.46−(7.3)2\sigma = \sqrt{57.46 - (7.3)^2} σ=57.46−53.29\sigma = \sqrt{57.46 - 53.29}
  4. Subtract the values.

    σ=4.17\sigma = \sqrt{4.17}
  5. Calculate the square root and round to two decimal places.

    σ≈2.04205778\sigma \approx 2.04205778 σ≈2.04\sigma \approx 2.04

    The standard deviation is 2.04 hours (correct to two decimal places).

    Standard Deviation=2.04\boxed{\text{Standard Deviation} = 2.04}
Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question