2026 NORTHBROOKS P1 Q23

Secondary 4

7 marks

The monthly electricity bills (to the nearest dollar) for 24 households in an HDB estate are shown in the stem-and-leaf diagram below.
Key: $7\mid3$ represent \$73.
1. Write down the median electricity bill.[1]
2. When the bill for a 25th household is added to the data, the range increases to \$52. Find the two possible values for this 25th household’s bill.[1]
This table represents the monthly household income distribution for a sample of 200 Singaporean households.
Monthly Income, $\$x$ Frequency $(f)$
$0<x\leq4000$ 30
$4000<x\leq8000$ 38
$8000<x\leq12000$ 40
$12000<x\leq16000$ 35
$16000<x\leq20000$ 25
$20000<x\leq30000$ 22
$x>30000$ 10
1. The maximum household income in this sample is \$50 000.
  1. Show that the estimated mean monthly household income for this group is \$12 890.[2]
  2. Hence, estimate the standard deviation of the household income. Give your answer correct to the nearest dollar.[1]
2. In the 2025 SingStat report, the median is often cited as a more “representative” figure than the mean for income. Based on the data given, explain why the mean might be higher than the median in this context.[1]
3. Find the probability that a household, chosen at random, has monthly income more than \$20 000.[1]

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Answer:(a)(i) \$82. (ii) \$56 or \$114. (b)(i)(a) \$12 890 (shown). (b) \$9211. (ii) High incomes pull the mean upwards. (iii) $\dfrac4{25}$.

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