Owning The Dataset
Table 1: Text Analysis
| Text Component |
Literal Content |
Simple Interpretation |
| Time period |
"For each of the first 11 months of last year" |
Data covers January through November of the previous year |
| Data subject |
"total number of transactions processed during the month" |
Each value is the complete transaction count for that month |
| Account owner |
"for Martina's bank account" |
All data is from Martina's personal bank account |
Table 2: Chart Analysis
| Chart Component |
What's Shown |
What This Tells Us |
| Chart type |
Vertical bar chart with 11 blue bars |
Each bar represents a month's transactions visually |
| Y-axis range |
Scale from 0 to 40 with gridlines every 5 units |
Monthly transactions range from 19 to 37 |
| Data completeness |
11 months shown (Jan-Nov), December missing |
The data set excludes December; only partial year is shown |
| Value variation |
Bars vary greatly in height (lowest 19, highest 37) |
Monthly transaction numbers fluctuate substantially |
Key Insights
The median number of monthly transactions for the 11 displayed months is 25; the missing December value will determine whether the yearly median stays at 25 or increases. The data varies between 19 and 37 transactions per month, showing uneven activity with no clear trend. December's missing value is required to finalize the yearly median.
Step-by-Step Solution
Question 1: Minimum Possible Median
Complete Statement:
Consistent with the information provided, the least that Martina's median monthly number of bank account transactions for the 12 months of last year could be is ______
Breaking Down the Statement
- Statement Breakdown 1:
- Key Phrase: median monthly number
- Meaning: The value exactly in the middle when all 12 months' transaction counts are sorted from least to greatest.
- Relation to Chart: There are 11 months with known values and 1 month (December) missing from the chart.
- Important Implications: The position where December's value is inserted into the sorted list will influence which values become the 6th and 7th (used to compute the median with 12 months).
- Statement Breakdown 2:
- Key Phrase: for the 12 months of last year
- Meaning: We must account for all twelve months, including the missing month (December).
- Relation to Chart: The chart provides only eleven values. We must consider all possibilities for December's value.
- Important Implications: We analyze the lowest possible median based on December taking the lowest feasible value.
What is needed: The smallest possible value for the 12-month median, given 11 fixed values and one unknown (December).
Solution:
- Condensed Solution Implementation:
Sort the 11 given values and insert December as the lowest possible value, then identify the 6th and 7th values which determine the median for a 12-month list.
- Necessary Data points:
Sorted known transactions: 19, 21, 22, 23, 25, 25, 27, 28, 29, 33, 37. December is missing.
- Calculations Estimations:
With December less than or equal to 19 (the smallest in the list), December becomes the new minimum: Dec,19,21,22,23,25,25,27,28,29,33,37. Positions 6 and 7 are both 25, so the median is \(\frac{25+25}{2} = 25\). Any December \(\leq 25\) still leaves both 6th and 7th as 25.
- Comparison to Answer Choices:
From the provided options [21, 22, 23, 24, 25], the minimum possible median is 25.
FINAL ANSWER Blank 1: 25
Question 2: Maximum Possible Median
Complete Statement:
and the greatest that it could be is ______
Breaking Down the Statement
- Statement Breakdown 1:
- Key Phrase: the greatest that it could be
- Meaning: What is the maximum possible value for the median?
- Relation to Chart: The median is maximized by placing December as the greatest value possible in the sorted order.
What is needed: The largest possible value for the 12-month median, given the data and the missing December value.
Solution:
- Condensed Solution Implementation:
Insert December as the largest possible value and find the 6th and 7th values for the 12-value sorted sequence.
- Necessary Data points:
Sorted known transactions: 19, 21, 22, 23, 25, 25, 27, 28, 29, 33, 37. December is missing.
- Calculations Estimations:
With December \(\geq 37\) (the largest known), December is added as the new maximum: 19,21,22,23,25,25,27,28,29,33,37,Dec. The 6th and 7th positions are 25 and 27, so the median is \(\frac{25+27}{2} = 26\). Any December value \(\geq 27\) shifts the positions for median to 25 and 27 as well.
- Comparison to Answer Choices:
From the available choices [25, 26, 27, 28], the maximum possible median is 26.
FINAL ANSWER Blank 2: 26
Summary
For this scenario, the minimum and maximum possible medians for the 12 months occur when the unknown December value is set at the lowest and highest possible values, respectively. With the given sorted data, the 6th and 7th positions in the 12-value list determine that the minimum median is 25 and the maximum is 26.
Question Independence Analysis
The questions are related and depend on the same dataset and logic: both blanks refer to the possible range of the median for the same year, depending on the value of the missing month. Calculation for each directly informs the other.
