Suppose that the class grade for a six-week period is based on three tests (T1, T2, T3), each of which counts for 15%, four quizzes (Q1, Q2, Q3, Q4), each of which counts for 10%. and a homework note book (HW), which counts for 15%. The grades are recorded in a spreadsheet similar to the one below. Which of the following formulae would NOT be a correct calculation of the six-week weighted average for Jatin?A B C D E F G H I J 1 Name T1 T2 T3 Q1 Q2 Q3 Q4 HW AVG 2 Jatin 87 92 80 76 79 87 74 90 3 Amit 91 85 77 78 88 96 90 92 4 Anil 65 72 70 80 81 74 77 80 5 Anita 96 88 91 76 91 100 74 98
Understanding Weighted Average Grade Calculation
This question asks us to identify a formula that does NOT correctly calculate a student's weighted average grade over a six-week period. The grade is based on multiple components, each with a specific weight.
Let's break down the components and their weights:
- Three Tests (T1, T2, T3): Each counts for 15% (or 0.15).
- Four Quizzes (Q1, Q2, Q3, Q4): Each counts for 10% (or 0.10).
- One Homework Notebook (HW): Counts for 15% (or 0.15).
The total weight is: $3 \times 15\% + 4 \times 10\% + 1 \times 15\% = 45\% + 40\% + 15\% = 100\%$.
Jatin's grades are listed in row 2 of the spreadsheet:
| Name | T1 (B2) | T2 (C2) | T3 (D2) | Q1 (E2) | Q2 (F2) | Q3 (G2) | Q4 (H2) | HW (I2) |
|---|---|---|---|---|---|---|---|---|
| Jatin | 87 | 92 | 80 | 76 | 79 | 87 | 74 | 90 |
Correct Weighted Average Formula
A weighted average is calculated by multiplying each grade by its corresponding weight and summing up these products. The general formula is:
$\text{Weighted Average} = (G_1 \times W_1) + (G_2 \times W_2) + \dots + (G_n \times W_n)$
Where $G_i$ is the grade for component $i$ and $W_i$ is the weight for component $i$.
For Jatin's grades, the correct formula in the spreadsheet would be:
= B2 * 0.15 + C2 * 0.15 + D2 * 0.15 + E2 * 0.10 + F2 * 0.10 + G2 * 0.10 + H2 * 0.10 + I2 * 0.15
This formula ensures each component's contribution is scaled correctly by its weight.
Analyzing the Given Formula Options
Let's examine each option provided and compare it to the correct weighted average calculation.
Option 1 Analysis
The formula is: = B2 * 0.15 + C2 * 0.15 + D2 * 0.15 + E2 * 0.1 + F2 * 0.1 + G2 * 0.1 + H2 * 0.1 + I2 * 0.15
This formula directly multiplies each grade by its corresponding weight (0.15 for tests/HW, 0.1 for quizzes) and sums the results. This is exactly the standard method for calculating a weighted average.
Analysis: Correct Calculation.
Option 2 Analysis
The formula is: =(B2 + C2 + D2 + I2)*0.15 + (E2 + F2 + G2 + H2)*0.1
This formula groups the three test grades (B2, C2, D2) and the homework grade (I2) together, summing them before multiplying by 0.15. It also groups the four quiz grades (E2, F2, G2, H2) together, summing them before multiplying by 0.1.
Let's expand this: $(B2 \times 0.15) + (C2 \times 0.15) + (D2 \times 0.15) + (I2 \times 0.15) + (E2 \times 0.1) + (F2 \times 0.1) + (G2 \times 0.1) + (H2 \times 0.1)$.
This is equivalent to the standard weighted average calculation where each test and the homework are weighted at 0.15 individually, and each quiz is weighted at 0.1 individually. This grouping is mathematically correct.
Analysis: Correct Calculation.
Option 3 Analysis
The formula is: =((B2 + C2 + D2 + I2)*1.5 + (E2 + F2 + G2 + H2)/10
This formula groups the tests and homework and multiplies their sum by 1.5. It groups the quizzes and divides their sum by 10.
- Multiplying by 1.5 is equivalent to multiplying by 150%. The required weight for tests and homework is 15% (0.15). This is a significant difference.
- Dividing by 10 is equivalent to multiplying by 0.1. The required weight for quizzes is 10% (0.1). This part is correct for the quiz component.
However, the test/homework component calculation is incorrect.
Analysis: Incorrect Calculation.
Option 4 Analysis
The formula is: =(B2 + C2 + D2 + I2)/15 + (E2 + F2 + G2 + H2)/10
This formula groups the tests and homework and divides their sum by 15. It groups the quizzes and divides their sum by 10.
- Dividing by 15 is equivalent to multiplying by $1/15$. The required weight for tests and homework is 15% (0.15 or $15/100$). Multiplying by $1/15$ is not the same as multiplying by $15/100$. $(1/15 \approx 0.0667$, while $15/100 = 0.15)$. This is incorrect for the test/homework component.
- Dividing by 10 is equivalent to multiplying by $1/10$ (or 0.1). The required weight for quizzes is 10% (0.1). This part is correct for the quiz component.
Since the test/homework component calculation is incorrect, the overall formula is incorrect.
Analysis: Incorrect Calculation.
Identifying the Incorrect Formula
Based on our analysis, Option 1 and Option 2 provide correct calculations for the weighted average. Option 3 and Option 4 provide incorrect calculations.
The question asks which formula would NOT be a correct calculation. Both Option 3 and Option 4 fit this description.
Comparing our analysis to the provided correct answer which points to Option 4, we confirm that Option 4 is indeed an incorrect formula for calculating the weighted average grade based on the specified weights.
Revision Table: Key Concepts
| Concept | Explanation |
|---|---|
| Weighted Average | A type of average where some data points contribute more than others to the final mean. Each data point is multiplied by its weight, and the products are summed and divided by the sum of the weights (which is typically 1 or 100% in grade calculations). |
| Percentage Weight | The proportion or importance assigned to each component. In this case, 15% for tests/HW and 10% for quizzes. Must sum to 100%. |
| Spreadsheet Formulas | Using cell references (like B2, C2) and mathematical operators (+, *, /) to perform calculations automatically in spreadsheet software. |
Additional Information on Grade Calculation
When calculating weighted averages, it's crucial to represent the weights correctly. Percentages like 15% must be converted to their decimal form (0.15) or fractional form (15/100) before multiplying by the grade. Dividing a sum of grades by a number like 15 (as seen in Option 4) is only correct if each grade in that sum was multiplied by a factor of $1/15$, which is not the weight specified for the tests or homework.
Grouping terms in a weighted average formula is valid as long as the multiplication by the correct decimal or fractional weight occurs correctly. For instance, summing up grades that share the same weight and then multiplying the sum by that weight is mathematically sound, as shown in Option 2.
Always double-check that the sum of all weights equals 100% (or 1.00) to ensure the average is calculated correctly across all components.
Important Questions from Types of Softwares
- Learning Management Systems (LMS) is a software application used for
Consider the following spreadsheet:
A B C 1 4 3 2 5 2 3 7 4 8 9 5 9 6 If the formula = $A3 + B2 in cell C4 is copied to cell C5, then what is the value in cell C5?
Given below are two statements:
Statement I: Shareware is a software that the users can try out for a trial period only. before being charged.
Statement II: Freeware is a software that the users can download free of charge. but they cannot modify the source code in any way.
In the light of the above statements. choose the correct answer from the options given below
In MS-EXCEL, Cell B9 contains the value 3, and B10 contains the value 6. You select both the cells and drag the fill handle down to B13. The contents of the cell B11, B12, and B13 will be ________
Consider the following MS-Excel spreadsheet in which the population column represents the city's population in millions of people :
A B C D E F 1. City State Population Haryana MP UP 2. Patiala Panjab 8.34 3. Sonipat Haryana 3.86 4. Noida UP 2.71 5. Indore MP 2.16 6. Mandi HP 1.49 7. Sagar MP 1.38 8. Panipat Haryana 1.39 9. Gwalior MP 1.24 Suppose the formula - IF($B2 = D$1, $A2, 0) is entered into cell D2 and then the cell D2 is copied and pasted to D2 : F9. How many cells in the range D2 : F9 contains 0?
