1. The problem involves analysis of given data sets for Impala observations and IQ scores, including arranging data, calculating mean, median, mode, and range, and interpreting results. Question 1 (Impala Observations): 1.1 Arrange in ascending order: $$21, 21, 21, 21, 25, 26, 28, 28, 30, 34, 34, 39, 40, 65, 80$$ 1.2 Arithmetic mean: Calculate sum: $$21+21+21+21+25+26+28+28+30+34+34+39+40+65+80 = 533$$ Number of data points $$n=15$$ $$\text{Mean} = \frac{533}{15} \approx 35.53$$ 1.3 Median: Since $$n=15$$ is odd, median is the $$\frac{15+1}{2} = 8^{th}$$ value in the ordered list. Median = 28 1.4 Mode: The value appearing most frequently is 21 (4 times). 1.5 Range: $$\text{Range} = 80 - 21 = 59$$ 1.6 Most appropriate central value: The mean is influenced by the high outlier 80, so median or mode better represent typical daily Impala counts. Median is preferred as it is the middle value and less affected by extremes. --- Question 3 (IQ Scores): 3.1 Arrange in ascending order: $$92, 97, 97, 97, 100, 103, 104, 105, 107, 107, 107, 107, 108, 112, 112, 112, 112, 114, 115, 116, 117, 117, 118, 122, 122, 127, 130, 137, 149$$ 3.2 Number of learners: $$n = 29$$ 3.3 Range: $$149 - 92 = 57$$ 3.4 Calculations: 3.4.1 Mean IQ Sum: $$92+97+97+97+100+103+104+105+107*4+108+112*4+114+115+116+117*2+118+122*2+127+130+137+149 = 3311$$ Mean = $$\frac{3311}{29} \approx 114.17$$ 3.4.2 Median: Position $$\frac{29+1}{2} = 15^{th}$$ value is 112 3.4.3 Mode: 107 and 112 both appear 4 times; modes: 107 and 112 (bimodal) 3.5 Frequency table: | Score Range | Frequency | |-------------|-----------| | 90 - 99 | 4 (92, 97x3) | | 100 - 109 | 7 (100, 103, 104, 105, 107x4, 108) | | 110 - 119 | 11 (112x4, 114, 115, 116, 117x2, 118) | | 120 - 129 | 4 (122x2, 127) | | 130 + | 3 (130, 137, 149) | Percentage with IQ $$\geq 110$$: $$\frac{11 + 4 + 3}{29} \times 100 \approx 62.07\%$$ --- Question 4 (Nellie's Marks): Marks: English 65, Additional Language 63, Social Sciences 75, Life Orientation 56, Technology 60, Arts and Culture 67, Natural Sciences 78, Economic and Management Sciences 80, Mathematics 84 (b) Mean mark: Sum: $$65+63+75+56+60+67+78+80+84 = 628$$ Number of subjects: 9 Mean = $$\frac{628}{9} \approx 69.78$$ (c) Range: $$84 - 56 = 28$$ (d) Is she a consistent achiever? Range is moderate (28), with some variation but mostly scores between mid-50s and mid-80s. She is fairly consistent but with room for improvement in some subjects. (e) Broken line graph is used to visualize trends and changes across ordered categories (subjects) clearly, making it easier to see increases or decreases in marks. Slug: "data statistics" Subject: "statistics" Desmos: {"latex":"","features":{"intercepts":true,"extrema":true}} q_count: 3