Question

The five most recent cricket scores of four teams are: \[ \begin{array}{c|ccccc} \text{Team 1} & 255 & 278 & 291 & 268 & 308 \\ \text{Team 2} & 301 & 282 & 269 & 299 & 279 \\ \text{Team 3} & 309 & 319 & 279 & 312 & 316 \\ \text{Team 4} & 288 & 301 & 322 & 310 & 289 \end{array} \] Based on this information, identify the team with the most consistent performance (least variance), and write its average.

Hint:

“Most consistent” \(=\) “least spread”. Use variance (or standard deviation) to compare spreads; the smallest value indicates the most consistent team.

Answer 1

Step 1: Compute the mean (average) for each team.
\(\displaystyle \overline{T1}=\frac{255+278+291+268+308}{5}=280\)
\(\displaystyle \overline{T2}=\frac{301+282+269+299+279}{5}=286\)
\(\displaystyle \overline{T3}=307,\;\; \overline{T4}=302\).
Step 2: Compare consistency via (population) variance.
\(\displaystyle \sigma^2=\frac{1}{5}\sum (x_i-\overline{x})^2\).
Quick calculation gives:
\(T1:\; \sigma^2=335.6\), \(T2:\; \sigma^2=149.6\), \(T3:\; \sigma^2=207.6\), \(T4:\; \sigma^2=166.0\).
Step 3: Decide.
Smallest variance is for Team 2, and its mean score is \(\boxed{286}\).