### Find standard deviation of distribution of a bar chart

Question Sample Titled 'Find standard deviation of distribution of a bar chart'

The bar chart shows the distribution of the numbers of calculators owned by some government officials. Find the standard deviation of the distribution correct to 2 decimal places.

A
${1.16}$
B
${1.38}$
C
${6.28}$
D
${2.24}$

 First find the mean of the distribution. Mean  $=\dfrac{{1}}{{31}}{\left({2}\times{0}+{9}\times{1}+{7}\times{2}+{9}\times{3}+{4}\times{4}\right)}$  $=\dfrac{{66}}{{31}}$ Recall that the stardard deviation of a grouped dataset${\left\lbrace{x}_{{1}};{n}_{{1}},{x}_{{2}};{n}_{{2}},\ldots,{x}_{{i}};{n}_{{i}}\right\rbrace}$ having mean ${m}$ and a total of ${n}$ data   $=\sqrt{{\dfrac{{1}}{{n}}{\left[{n}_{{1}}{\left({x}_{{1}}-{m}\right)}+{n}_{{2}}{\left({x}_{{2}}-{m}\right)}+\ldots+{n}_{{i}}{\left({x}_{{i}}-{m}\right)}\right]}}}$ Standard deviation  $=\sqrt{{\dfrac{{1}}{{31}}{\left[{2}{\left({0}-\dfrac{{66}}{{31}}\right)}+{9}{\left({1}-\dfrac{{66}}{{31}}\right)}+{7}{\left({2}-\dfrac{{66}}{{31}}\right)}+{9}{\left({3}-\dfrac{{66}}{{31}}\right)}+{4}{\left({4}-\dfrac{{66}}{{31}}\right)}\right]}}}$  $={1.1568013598091036}$  $={1.16}$(cor. to 2 d.p.)

 For Casio fx-50FH II$:$ Under the Statistical Mode (SD), input the data into the calculator. Before inputing the data, you may need to clear the previously stored data using CLR Stat. [Shift] ${\left[{9}\right]}$ ${\left[{1}\right]}$ [EXE] For example, the first bar corresponds to inputing ${0}$ having frequency ${2}.$ ${\left[{0}\right]}{\left[;\right]}{\left[{2}\right]}$ [M+] The second bar corresponds to inputing ${1}$ having frequency ${9}.$ ${\left[{1}\right]}{\left[;\right]}{\left[{9}\right]}$ [M+] Continue the above steps with the remaining data. And check the standard deviation $\sigma_{{x}}$under S-VAR$.$ [Shift] ${\left[{2}\right]}$ ${\left[{2}\right]}$ [EXE] The displayed standard deviation  $={1.1568013598091036}$  $={1.16}$(cor. to 2 d.p.)

# 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