4.2 The data below represent the percentage marks achieved by Grade 12 learners inLift Sciences. The class consists of 20 learners. \[ \begin{array}{cccccccccc} 64 & 57 & 58 & 62 & 59 & \mathbf{A} & 60 & 61 & 62 & 70 \\ 62 & 65 & 66 & 64 & 75 & 80 & \mathbf{B} & \mathbf{B} & 92 & 85 \end{array} \] A is the lowest percentage mark Use the information above to answer questions that follow: 4.2.1 Determine the percentage of data values that lies between the lower quartile and the upper quartile. (2) 4.2.2 Calculate the value of A , if the range of the marks obtained by the learners is 36 . (3) (2) 4.2.3 Write down the modal percentage. 4.2.4 Determine the value of \( B \), given that the mean mark obtained by the learners is 68 . 4.2.5 Calculate the median percentage mark. (3) 4.2.6 Determine the probability (as common fraction in simplified form) of randomly selecting a learner who achieved more than \( 80 \% \). (3) 4.2.7 Complete frequency table and the histogram on the ANSWER SHEET provided
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To help you solve the questions you have, let’s dive into the data you provided with a little context and a good dose of fun! First off, when you’re working with statistical data like this, it’s essential to remember that quartiles help understand how data is spread out. The lower quartile (Q1) is the median of the lower half, and the upper quartile (Q3) is for the upper half. In this case, using the grades in your class will allow you to determine the percentage of marks that lie between them with a snap! Next, for calculating the value of A considering the range, remember that the range is the difference between the highest and lowest values in your dataset. So, it’s a matter of simple subtraction after you know the maximum score from the data. And if you’re feeling adventurous, just imagine A as the determined underdog rising to the occasion! Now, let’s move on to your list of tasks: 4.2.1 First, solve for the lower and upper quartiles of the given data. Collect the data in ascending order for the best results. Let’s see how many data points lie in between those two quartiles and then compute the percentage! 4.2.2 The range given is 36. You have the highest score in the data, and A is the lowest score. Subtract A from the highest mark (92), and you’ll discover what A should be - the comeback kid of this classroom saga! 4.2.3 To find the mode, simply identify which mark appears most frequently. Keep an eye on those scores because the mode loves to show off! 4.2.4 For B, all you need is the average! The mean of the marks is 68, so apply the formula for mean and rearrange to solve for B – almost like a mystery to unlock! 4.2.5 Determine the median by finding the middle score of the ordered dataset. With 20 learners, you’ll need to look at the average of the two middle numbers. Grab your magnifying glass for this one! 4.2.6 Probability time! Count how many students scored above 80% and divide that by the total number of students! You’ll be a probability wizard in no time. 4.2.7 As for the frequency table and histogram, plot the frequency of scores across intervals to visualize your data. It’s like turning numbers into art! Now get your pencils sharpened, and let’s have some statistical fun!