Draw bar diagram for this data: X 0 1 2 3 4 5 6 7 8 9 10 Y 0 5 10 8 6 4 2 2 1 1 1

Use your GDC to sketch a bar chart for this data: X 0 1 2 3 4 5 6 7 8 9 10 Y 0 5 10 8 6 4 2 2 1 1 1 Bar graph is a method of presenting data by drawing rectangular bars of equal width and with equal space between the two bars. Bar graphs can be drawn using horizontal or vertical bars Bar chart for given data is: Let us take the values of X on the X -axis with width 1 unit and the values of Y on the Y -axis with the width 1 unit.

Given: x 0 1 2 3 4 5 6 7 8 9 10 f 0 5 10 8 6 4 2 2 1 1 1 Use your GDC to sketch a box plot.

Use your GDC to sketch a bar chart for this data: x 0 1 2 3 4 5 6 7 8 9 10 f 0 5 10 8 6 4 2 2 1 1 1 Data values along with cumulative frequency: x 0 1 2 3 4 5 6 7 8 9 10 f 0 5 10 8 6 4 2 2 1 1 1 Cumulative frequency 0 5 15 23 29 33 35 37 38 39 40 Median: Here there are 40 data values, which is even. See in the cumulative frequencies, the value just greater than average of N 2 th and N 2 + 1 th data values corresponding to value of x is median. ⇒ Median is average of 40 2 th and 40 2 + 1 th data values = Average of 20 th and 21 th data values. So, Median = 3 + 3 2 = 3 Hence, the median of the given data is 3 . Now, lower quartile Q 1 is the median of the lower 50 % of the data. Here, there are 40 data values, which is even. See in the cumulative frequencies, the value just greater than average of N 4 th and N 4 + 1 th data values, corresponding to value of x is Q 1 . ⇒ Lower quartile is average of 40 4 th and 40 4 + 1 th data values = Average of 10 th and 11 th data values. So, Q 1 = 2 + 2 2 = 2 Hence, the lower quartile or first quartile of the given data is 2 . Now, upper quartile Q 3 is the median of the upper 50 % of the data. Here, there are 40 data values, which is even. See in the cumulative frequencies, the value just greater than average of 3 N 4 th and 3 N 4 + 1 th data values, corresponding to value of x is Q 3 . ⇒ Upper quartile is average of 3 × 40 4 th and 3 × 40 4 + 1 th data values = Average of 30 th and 31 th data values. So, Q 3 = 5 + 5 2 = 5 Hence, the upper quartile of the given data is 5 . Here, obtained results are Minimum First quartile Median Third quartile Maximum 0 2 3 5 10 Make a box by drawing horizontal lines connecting the quartiles. Connect the top or the first quartile to the top of the third quartile, going through the median. Connect the bottom of the first quartile to the bottom of the third quartile, making sure to go through the median. General diagram of Box and whisker plot: Thus, the box-and whisker plot for the given data:

Given: x 0 1 2 3 4 5 6 7 8 9 10 f 0 5 10 8 6 4 2 2 1 1 1 and its box plot is Describe the skew of the data.

Given: x 0 1 2 3 4 5 6 7 8 9 10 f 0 5 10 8 6 4 2 2 1 1 1 Box plot : We know that, if the longer part of the box is to the right (or above) the median, the data is said to be skewed right. If the longer part is to the left (or below) the median, the data is skewed left. Here, from the box plot it is clear that the data is longer to the right (or above) the median, Thus, the data is said to be skewed right.

Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Data: Statistics for Univariate Data, Exercise 29: Exercise 6G

Author:Natasha Awada, Paul La Rondie, Laurie Buchanan & Jill Stevens

Natasha Awada Mathematics Solutions for Exercise - Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Data: Statistics for Univariate Data, Exercise 29: Exercise 6G

Attempt the free practice questions on Chapter 6: Representing Data: Statistics for Univariate Data, Exercise 29: Exercise 6G with hints and solutions to strengthen your understanding. Mathematics : Analysis and Approaches Standard Level Course Companion solutions are prepared by Experienced Embibe Experts.

Questions from Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Data: Statistics for Univariate Data, Exercise 29: Exercise 6G with Hints & Solutions

HARD

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6G>Q 3

The number of students in international schools in the country of Portmany is shown below.
$20, 600, 650, 710, 790, 800, 855, 878, 943, 990, 1000, 1500, 1700, 1850, 2000, 2150, 2400, 2500, 2135, 6000$

Given that $6000$ is an outlier. State a reason to remove the outlier.

HARD

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6G>Q 3

Test scores for an IB morning exam are:
$99, 56, 78, 55.5, 32, 90, 80, 81, 56, 59, 45, 77, 84.5, 84, 70, 72, 68, 32, 79, 90$ ,

Test scores for an IB afternoon exam are:
$98, 78, 68, 83, 81, 89, 88, 76, 65, 45, 98, 90, 80, 84.5, 85, 79, 78, 98, 90, 79, 81, 25.5$

Draw a box-and-whisker plot for each data set. Use one number line for both plots, and draw one above the other.

HARD

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6G>Q 4

Test scores for an IB morning exam are:
$99, 56, 78, 55.5, 32, 90, 80, 81, 56, 59, 45, 77, 84.5, 84, 70, 72, 68, 32, 79, 90$ ,

Test scores for an IB afternoon exam are:
$98, 78, 68, 83, 81, 89, 88, 76, 65, 45, 98, 90, 80, 84.5, 85, 79, 78, 98, 90, 79, 81, 25.5$

Given a box-and-whisker plot for each data set using one number line for both plots, having the test scores for an IB morning exam first and under it lies the test scores of IB afternoon scores box plot.

Question Image

State which examination has the greatest spread for the middle $50 %$ .

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6G>Q 4

Test scores for an IB morning exam are:
$99, 56, 78, 55.5, 32, 90, 80, 81, 56, 59, 45, 77, 84.5, 84, 70, 72, 68, 32, 79, 90$ ,

Test scores for an IB afternoon exam are:
$98, 78, 68, 83, 81, 89, 88, 76, 65, 45, 98, 90, 80, 84.5, 85, 79, 78, 98, 90, 79, 81, 25.5$

Question Image

Describe from the given that morning exam has the greatest spread for the middle $50 %$ , tells us about the range in performance for the two exams.

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6G>Q 4

Draw bar diagram for this data:

$X$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$Y$	$0$	$5$	$10$	$8$	$6$	$4$	$2$	$2$	$1$	$1$	$1$

MEDIUM

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6G>Q 5

Given:

$x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$f$	$0$	$5$	$10$	$8$	$6$	$4$	$2$	$2$	$1$	$1$	$1$

Use your $GDC$ to sketch a box plot.

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6G>Q 5

Given:

$x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$f$	$0$	$5$	$10$	$8$	$6$	$4$	$2$	$2$	$1$	$1$	$1$

and its box plot is

Question Image

Describe the skew of the data.

EASY

Diploma

IMPORTANT

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 6 - Representing Data: Statistics for Univariate Data>Exercise 6G>Q 7

The time, in minutes, taken by $100$ students to reply to their friends on social media is shown as a cumulative frequency curve. Find the longest time taken to reply.(Answer without units)

Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Data: Statistics for Univariate Data, Exercise 29: Exercise 6G

Natasha Awada Mathematics Solutions for Exercise - Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Data: Statistics for Univariate Data, Exercise 29: Exercise 6G

Questions from Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Data: Statistics for Univariate Data, Exercise 29: Exercise 6G with Hints & Solutions

Learn and Prepare for any exam you want !