Stem-and-leaf diagram, mean, median

Question Sample Titled 'Stem-and-leaf diagram, mean, median'

Noah conducts a survey on the numbers of micro films watched in a month by students. Questionnaires are sent out and twenty three of them are returned. The stem-and-leaf diagram below shows the numbers of micro films recorded in the twenty three questionnaires:

Stem (tens)Leaf (units)
 ${0}$ ${1}$ ${2}$
 ${0}$ ${0}$ ${0}$ ${2}$ ${3}$ ${4}$ ${4}$ ${4}$ ${4}$ ${5}$ ${5}$ ${6}$ ${6}$ ${7}$ ${8}$ ${8}$ ${8}$ ${0}$ ${1}$ ${1}$ ${3}$ ${8}$ ${4}$

 (a) Find the mean and the median of the numbers of micro films recorded in the twenty three questionnaires. (2 marks) (b) Noah receives six more questionnaires. He finds that the mean of the numbers of micro films recorded in these six questionnaires is ${7}$. It is found that the numbers of micro films recorded in three of these six questionnaires are ${8}$ , ${8}$ and ${9}$ .  (4 marks) (i) Write down the mean of the numbers of micro films recorded in the twenty nine questionnaires. (ii) Is it possible that the median of the numbers of micro films recorded in the twenty nine questionnaires is the same as the median found in (a)? Explain your answer.

 (a) The mean$={7}$ 1A The median$={6}$ 1A (b) (i) The mean$={7}$ 1A (ii) Let ${a}$ , ${b}$ and ${c}$ be the numbers of micro films recorded in the three other questionnaires. Note that $\dfrac{{{a}+{b}+{c}+{8}+{8}+{9}}}{{6}}={7}$ 1M Therefore, we have ${a}+{b}+{c}={17}$ If the two medians are the same, then we have ${a}\le{6}$ , ${b}\le{6}$ and ${c}\le{6}$ . 1M i.e. ${a}+{b}+{c}\le{18}$ . It is possible since ${a}+{b}+{c}={17}$ . Thus, it is possible that the two medians are the same.  1A f.t.

專業備試計劃

Level 4+ 保證及 5** 獎賞

ePractice 會以電郵、Whatsapp 及電話提醒練習

ePractice 會定期提供溫習建議

Level 5** 獎勵：會員如在 DSE 取得數學 Level 5** ，將獲贈一套飛往英國、美國或者加拿大的來回機票，唯會員須在最少 180 日內每天在平台上答對 3 題 MCQ。

Level 4 以下賠償：會員如在 DSE 未能達到數學 Level 4 ，我們將會全額退回所有會費，唯會員須在最少 180 日內每天在平台上答對 3 題 MCQ。

FAQ

ePractice 是甚麼？

ePractice 是一個專為中四至中六而設的網站應用程式，旨為協助學生高效地預備 DSE 數學（必修部分）考試。由於 ePractice 是網站應用程式，因此無論使用任何裝置、平台，都可以在瀏覽器開啟使用。更多詳情請到簡介頁面。

ePractice 可以取代傳統補習嗎？

1. 會員服務期少於兩個月；或
2. 交易額少於 HK\$100。

Initiating...

HKDSE 數學試題練習平台