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Q9. SGR
Expert-verifiedWhich measure of central tendency best represents the data? Justify your answer. Then find the measure.
Sophia keeps track of the ages of students in her class. She wants to best represent the ages of her classmates: 13, 14, 13, 13, 14, 13, 13, 15, 14, 13, 14, 14, 10.
The best measure of central tendency to represent the data is median of the data and the value of median is 13.
A measure of central tendency is a summary statistic that represents the center point or typical value of a datasheet.
The 3 most common measures of central tendency are the mean, median and mode.
The median is the middle number in a sorted, ascending or descending, list of numbers.
Median $={\left(\frac{n+1}{2}\right)}^{\text{th}}$ term, if the number of values in data sheet $\left(n\right)$ is odd.
Median $=\frac{{\left(\frac{n}{2}\right)}^{\text{th}}\text{term}+{\left(\frac{n}{2}+1\right)}^{\text{th}}\text{term}}{2}$, if the number of values in data sheet $\left(n\right)$ is even.
The ages of the classmates are: 13, 14, 13, 13, 14, 13, 13, 15, 14, 13, 14, 14, 10
List the data in ascending order.
10, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15
Observe the data.
There is one value 15 that is greater than the other values and also there is not a big gap in the middle of the data.
So, median would best represent the data.
The number of data values $\left(n\right)=13$ (odd)
Hence,
Median $={\left(\frac{n}{2}+1\right)}^{\text{th}}$ term
Substitute $n=13$.
Median $={\left(\frac{13+1}{2}\right)}^{\text{th}}$ term
Median $={\left(\frac{14}{2}\right)}^{\text{th}}$ term
Median $={\left(7\right)}^{\text{th}}$ term
Median $=13$
Therefore, the best measure of central tendency to represent the data is median of the data and the value of median is 13.
The results of a simulation of coin flipping are shown.
Outcome | Frequency |
heads | 25 |
tails | 75 |
What is the theoretical probability of heads?
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