题目

Problem

The stem and leaf diagram below shows the ages (in years) of the residents in a care home.

Key: $4\mid3$ is an age of 43

(a) Find the median age of the residents.

(1)

(b) Find the interquartile range (IQR) of the ages of the residents.

(2)

An outlier is defined as a value that is either more than $1.5\times(\text{IQR})$ below the lower quartile or more than $1.5\times(\text{IQR})$ above the upper quartile.

(3)

(d) On the grid on page 5, draw a box plot to summarise these data.

(3)

解答

(a)

解法一

思路

展开

共有 30 个数据，中位数是第 15 个与第 16 个数据的平均值。

答题过程

展开

There are $30$ values, so the median is the mean of the 15th and 16th values.

From the stem and leaf diagram, both are $74$ .

Therefore the median is

\begin{align*} 74. \end{align*}

(b)

解法一

思路

展开

下四分位数和上四分位数分别是下半部分和上半部分的中位数。

答题过程

展开

From the ordered data,

\begin{align*} Q_1=68,\qquad Q_3=80. \end{align*}

Hence

\begin{align*} \operatorname{IQR}=80-68=12. \end{align*}

(c)

解法一

思路

展开

先算离群值边界，再检查数据里是否有低于下界或高于上界的值。

答题过程

展开

The lower boundary is

\begin{align*} Q_1-1.5(\operatorname{IQR})=68-1.5(12)=50. \end{align*}

The upper boundary is

\begin{align*} Q_3+1.5(\operatorname{IQR})=80+1.5(12)=98. \end{align*}

Outliers are values less than $50$ or greater than $98$ .

Therefore the only outlier is

\begin{align*} 43. \end{align*}

(d)

解法一

思路

展开

箱线图的盒子用 $Q_1=68$ 、中位数 $74$ 、 $Q_3=80$ 。因为 43 是离群值，所以左须画到非离群最小值 54，右须画到 97。

答题过程

展开

Draw a box from $68$ to $80$ , with the median line at $74$ .

Draw whiskers to $54$ and $97$ , and show $43$ separately as an outlier.

IAL 2021 Jan Q2

题目

解答

(a)

解法一

思路

答题过程

(b)

解法一

思路

答题过程

(c)

解法一

思路

答题过程

(d)

解法一

思路

答题过程