Question:
The distance (in meter) for 7 throws of a shotputter are \(14.5,15.2,16.8,17.1,15.9,16.3,14.7\). Calculate sample mean and sample standard deviation.
The distance (in meter) for 7 throws of a shotputter are \(14.5,15.2,16.8,17.1,15.9,16.3,14.7\). Calculate sample mean and sample standard deviation.
Show Hint
For sample standard deviation always divide by \(n-1\), not by \(n\).
Updated On: Jun 11, 2026
- \(14.79,\;0.88\)
- \(15.79,\;1.02\)
- \(14.79,\;1.15\)
- \(15.79,\;0.96\)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Find the sample mean.
\[ \bar x = \frac{14.5+15.2+16.8+17.1+15.9+16.3+14.7}{7} \] \[ = \frac{110.5}{7} \] \[ = 15.7857 \] \[ \bar x\approx15.79. \]
Step 2: Compute deviations from mean and square them.
After calculation, \[ \sum (x_i-\bar x)^2 \approx5.49. \]
Step 3: Calculate sample standard deviation.
\[ s = \sqrt{\frac{\sum(x_i-\bar x)^2}{n-1}} \] \[ = \sqrt{\frac{5.49}{6}} \] \[ = \sqrt{0.915} \] \[ \approx0.96. \] Therefore, \[ \boxed{(\bar x,s)=(15.79,\;0.96)} \]
\[ \bar x = \frac{14.5+15.2+16.8+17.1+15.9+16.3+14.7}{7} \] \[ = \frac{110.5}{7} \] \[ = 15.7857 \] \[ \bar x\approx15.79. \]
Step 2: Compute deviations from mean and square them.
After calculation, \[ \sum (x_i-\bar x)^2 \approx5.49. \]
Step 3: Calculate sample standard deviation.
\[ s = \sqrt{\frac{\sum(x_i-\bar x)^2}{n-1}} \] \[ = \sqrt{\frac{5.49}{6}} \] \[ = \sqrt{0.915} \] \[ \approx0.96. \] Therefore, \[ \boxed{(\bar x,s)=(15.79,\;0.96)} \]
Was this answer helpful?
0
0
Top NIMCET Mathematics Questions
- Among the given numbers below, the smallest number which will be divided by 9, 10, 15 and 20 and leaves the remainders 4, 5, 10 and 15, respectively, is:
- If one AM (Arithmetic mean) \( a \) and two GM's (Geometric means) \( p \) and \( q \) be inserted between any two positive numbers, the value of \( p^3 + q^3 \) is:
- If one AM (Arithmetic mean) \( a \) and two GM's (Geometric means) \( p \) and \( q \) be inserted between any two positive numbers, the value of \( p^3 + q^3 \) is:
- A coin is thrown 8 times. What is the probability of getting a head in an odd number of throws?
- The value of \( \tan\left(\frac{\pi}{4} + \theta\right) \times \tan\left(\frac{3\pi}{4} + \theta\right) \) is:
View More Questions
Top NIMCET Probability and Statistics Questions
- The scores of students in a national level examination are normally distributed with a mean of 500 and a standard deviation of 100. If the value of the cumulative distribution of the standard normal random variable at 0.5 is 0.691, then the probability that a randomly selected student scored between 450 and 500 is:
- Which one of the following is NOT a correct statement?
- The number of accidents per week in a town follows a Poisson distribution with mean 2. If the probability that there are three accidents in two weeks time is \( k e^{-6} \), then the value of \( k \) is:
- The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2, and 6, then the mean deviation from the mean of the data is:
- The 10th and 50th percentiles of the observation 32, 49, 23, 29, 118 respectively are
View More Questions
Top NIMCET Questions
- How much work is done to slide a crate for a distance of 25 m along a loading dock by pulling on it with a 180 N force where the dock is at an angle of \(45^\circ\) from the horizontal?
- Let \( f : \mathbb{R} \to \mathbb{R} \) be a function such that \( f(0) = \frac{1}{\pi} \) and \( f(x) = \frac{x}{e^x - 1} \) for \( x \ne 0 \). Then:
- The value of the limit \[ \lim_{x \to 0} \left( \frac{1^x + 2^x + 3^x + 4^x}{4} \right)^{\frac{1}{x}} \] is:
- Consider the function \( f(x) = x^{2/3} \cdot (6 - x)^{1/3} \). Which of the following statements is false?
- Lines \( L_1, L_2, \dots, L_{10} \) are distinct, among which the lines \( L_2, L_4, L_6, L_8, L_{10} \) are parallel to each other, and the lines \( L_1, L_3, L_5, L_7, L_9 \) pass through a given point \( C \). The number of points of intersection of pairs of lines from the complete set \( L_1, L_2, L_3, \dots, L_{10} \) is:
View More Questions