Question:
What is the standard deviation of the given data set:
25, 50, 45, 30, 70, 42, 36, 48, 34, 60 (correct to two decimal places).
What is the standard deviation of the given data set: 25, 50, 45, 30, 70, 42, 36, 48, 34, 60 (correct to two decimal places).
Show Hint
Standard deviation measures how spread out numbers are from the mean. Use variance = average of squared differences, then take square root.
Updated On: Apr 24, 2025
- 13.33
- 13.31
- 13.14
- 13.08
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
First, compute the mean:
Mean = $\dfrac{25 + 50 + 45 + 30 + 70 + 42 + 36 + 48 + 34 + 60}{10} = \dfrac{440}{10} = 44$
Now compute the squared deviations:
$\sum (x_i - \bar{x})^2 = (25-44)^2 + (50-44)^2 + \ldots + (60-44)^2 = 1710$
Variance = $\dfrac{1710}{10} = 171$
Standard Deviation = $\sqrt{171} \approx 13.08$
Was this answer helpful?
0
0
Top Questions on Statistics
- The mean deviation from the median for the following data is:
\[ \begin{array}{c|ccccc} x_i & 9 & 3 & 7 & 2 & 5 \\ f_i & 1 & 6 & 2 & 8 & 4 \\ \end{array} \]- AP EAPCET - 2025
- Mathematics
- Statistics
- Two students appeared simultaneously for an entrance exam. If the probability that the first student gets qualified in the exam is \( \frac{1}{4} \) and the probability that the second student gets qualified in the same exam is \( \frac{2}{5} \), then the probability that at least one of them gets qualified in that exam is
- AP EAPCET - 2025
- Mathematics
- Statistics
Variance of the following discrete frequency distribution is:
\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Class Interval} & 0-2 & 2-4 & 4-6 & 6-8 & 8-10 \\ \hline \text{Frequency (}f_i\text{)} & 2 & 3 & 5 & 3 & 2 \\ \hline \end{array} \]- AP EAPCET - 2025
- Mathematics
- Statistics
- The mean and variance of the observations \( x_1, x_2, x_3, \dots, x_{15} \) are respectively 2 and 4. If the mean and variance of the observations \( Y_1, Y_2, \dots, Y_{10} \) are respectively 2 and 5, then the variance of the observations \( x_1, x_2, \dots, x_{15}, Y_1, Y_2, \dots, Y_{10} \) is:
- AP EAPCET - 2025
- Mathematics
- Statistics
- The mean and variance of the observations \( x_1, x_2, x_3, \dots, x_{15} \) are respectively 2 and 4. If the mean and variance of the observations \( Y_1, Y_2, \dots, Y_{10} \) are respectively 2 and 5, then the variance of the observations \( x_1, x_2, \dots, x_{15}, Y_1, Y_2, \dots, Y_{10} \) is:
- AP EAPCET - 2025
- Mathematics
- Statistics
View More Questions
Questions Asked in NPAT exam
- A can draw 10 illustrations in 5 days. B is three times as productive in twice the amount of time (in comparison to A). How many illustrations can B draw in a day?
- NPAT - 2025
- Time and Work
- Based on the given image, which of the following options must be true?
- NPAT - 2025
- Visual Reasoning
- A, B and C have some marbles. The ratio of the number of marbles with A to the number with B is 2:1. Also, the number of marbles with A to the number with C is 1:4. What is the approximate percentage of the total number of marbles that are with C?
- NPAT - 2025
- Percentages
- If \( p \) and \( q \) are numbers such that the pair of linear equations \( (p + 2)x + (q - 1)y = 10 \) and \( (q + 2)x + (p - 1)y = 10 \) have infinite solutions for \( x \) and \( y \), then \( p = q \).
- NPAT - 2025
- Linear Equations
- If \( x \), \( y \), and \( z \) are positive integers and \( p = \left( \left( (x - 1)^2 / |x| \right) + 2 \right) + \left( \left( (y - 1)^2 / |y| \right) + 2 \right) + \left( \left( (z - 1)^2 / |z| \right) + 2 \right), \) then \( p<6 \).
- NPAT - 2025
- Algebra
View More Questions