Organising, Representing and Interpreting Data

Think-pair-share, Group discussions, Talk for Learning and experiential learning.
Learning Experience: Learners in mixed-ability groups discuss measures of central tendencies, how to calculate them given grouped and ungrouped data, and discover which is appropriate to report on a given data.
Activity 1:
- Learners in pairs identify the measures of central tendencies they have encountered previously as mode, median and mean.
- Learners in pairs establish that mode median and mean are also known as averages and can be used to describe data.
- Learners in pairs recollect the concept of mode, median and mean and how to calculate the three measures of central tendencies given raw data.
Example 1: Find the mode, median and mean of 3,20,5,7,18,16,5,11,4,5,3.
- Learners in pairs recollect that mode is the value that occurs most frequently in a given data. Therefore, the mode in Example 1 is 5.
- Learners in pairs recollect the median is the middle value when data is arranged in ascending or descending order, and the number of values is odd. Therefore, the data in example 1 needs to be arranged as 3,3,4,5,5,5,7,11,16,18,20. Therefore, the median value is 5.
- Learners further discover that when the number data is even, then the median= OX# PI #L<<_N GhP M&_XNO )
Example 2: Find the median of 3,5,7,9,11,13. 7$2 Solution: Median= ) = 9
- Learners in pairs recollect that the mean, for Example 1 is calculated as "$"$,$.$.$.$7$!!$!/$!1$)( = 8.818. Therefore, the mean is approximately 8.8 !!
- Learners in pairs solve practical examples of measures of central tendencies.
Example 1: Akua is an Art student, The following are her scores for the first term examinations: 58,67,60,84,93,97,98. Calculate her mean score.
.1$/7$/($1,$2"$27$21 Solution: Akua's mean score = 7 = 79.6 Activity 2:
- Learners in groups extend their knowledge in finding measures of central tendencies of raw data to grouped and ungrouped data.
- Learners in groups first brainstorm how to calculate measures of central tendencies of ungrouped data where some of the values are repeating.
- Learners to solve practical examples using real data.
Activity 3:
- Learners in groups extend their knowledge and conceptualise finding measures of central tendencies of grouped data.
- Learners apply their knowledge and understanding of grouped data to construct a frequency table and calculate the measures of central tendency. Example 1: The data below shows the mass of 40 students in a class. The measurement is to the nearest kg.
55 70 57 73 55 59 64 72 60 48 58 54 69 51 63 78 75 64 65 57 71 78 76 62 49 66 62 76 61 63 63 76
52 76 71 61 53 56 67 71
- Construct a frequency table for the data using the 45-49, 50-54, etc.
- Calculate the mean, mode and median.
Solution
- Learners in groups construct a frequency table with the details of grouped data.
Class Class 𝑓 Mass Frequency (kg) boundaries mark (𝑥) 44.5-49.5 47 94 45 -49 2 49.5-54.5 52 208 50 -54 4
55 -59 7 54.5-59.5 57 399
59.5-64.5 62 620 60 -64 10
65 -69 4 64.5-69.5 67 268
70 -74 6 69.5-74.5 72 432
75-79 7 74.5-79.5 77 539
∑𝑓 = 40 ∑𝑓 = 2560
- ∑I0 Learners calculate the mean (direct mean) using the formula 𝑀 l𝑥n = ∑I
- )./( 𝑥 = ,(
- 𝑥 = 64 𝑘
- Learners in groups identify the mode by inspection and by using a formula.
- By inspection identify 62 as the mode.
- By formula ∆
- 𝑚 = 𝐿 ! + i $ j 𝐶 ∆ $∆ $ ! Where 𝐿 ! =Lower class boundary of the modal class,
∆ ! =excess frequency of modal class over the frequency of the next lower class. ∆ ) =excess frequency of modal class over the frequency of the next higher class, and 𝐶=size of modal class
- Applying the formula to solve the mode, "
- Mode = 59.5 + i j × 4 "$,
- ≈ 61.2143
Therefore, the mode is 62 to the nearest whole number.
- Learners in groups brainstorm to find the median. Learners apply the formula 𝑚 = 𝐿 ! + $ B*∑g $ u ! v 𝐶 g %
Where, 𝐿 ! = the lower class boundary of the median class; 𝑁 = total frequency; ∑𝐹 ! = sum of frequencies of all classes lower than the median class; 𝐹 # = frequency of the median class; 𝐶 = the size of the median class.
- Applying the formula in their collaborative group 1 (40) − 13 𝑀 = 59.5 + Ò 2 Ó×4 10
𝑀 = 62.3
- Learners in groups brainstorm to calculate the assumed mean formula, which is ∑I< 𝑥 = 𝐴 + ∑I
where, 𝐴 =the assumed mean 𝑑 = 𝑥 − 𝐴, which is the deviation from the assumed mean.
Deviation 𝑓 L 𝑑 L Mass 𝑓 L Class (𝑑) (kg) mark (𝑥 L ) 𝑥 − 𝐴 L −30 47 47 − 62 = −15 45 -49 2
52 − 62 = −10 −40 50 -54 4 52
57 57 − 62 = −5 −35 55 -59 7
60 -64 10 62 62 − 62 = 0 0 65 -69 4 67 67 − 62 = 5 20
70 -74 6 72 72 − 62 = 10 60
75-79 7 77 77 − 72 = 5 35
∑𝑓 =40 ∑𝑓=10
- Learners in groups select the central value as the assumed mean. With regard to the question, the assumed mean is 62.
- Learners in groups determine the values in the table and find the totals needed.
- Once the totals are found, learners go ahead and calculate the assumed mean !( 1. 𝑥 = 62 + ,( 2. 𝑥 = 62.4
Activity 3:
- Research work on how to select the assumed mean.
- Learners in groups research how to select the assumed mean and share findings with the whole class.
Teaching and Learning Resources:
- SHS curriculum
- Research journals
- Internet or e-books
- Real-life examples
- Software (Excel, SPSS)
Assessment (1.4.1.AS.7). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning.